Perform the indicated oprrations and then simply.
w-2/w -8 - w + 2/w + 8 + w - 104/w^2 -64
I assume this means
(w-2)/(w-8) - (w+2)/(w+8) + (w-104)/(w^2-64)
Placing everything ove a common denominator (w^2-64) = (w-8)(w+8) we then have a numerator of
(w-2)(w+8) - (w+2)(w-8) + (w-104)
= w^2 + 6w - 16 - (w^2 - 6w - 16) - w + 104
= 11w + 104
So, the result is (11w + 104)/(w^2 - 64)
To simplify the given expression, we need to combine like terms and simplify any fractions. Let's break it down step by step:
w - 2/w - 8 - w + 2/w + 8 + w - 104/w^2 - 64
1. Combine like terms within each set of parentheses:
(w - 2)/w - 8
- (w + 2)/w + 8
+ w - 104/w^2 - 64
2. Now, let's focus on the fractions. To combine fractions, we need the same denominator:
1) For (w - 2)/w - (w + 2)/w, the denominators are already the same (w), so we can combine the numerators:
(w - 2 - w - 2)/w = (-4)/w
2) For -104/w^2, -104 is the numerator, and w^2 is the denominator. To combine this with the previous fractions, we need to express -104 as having a denominator of w^2. We multiply the numerator and denominator by w^2:
(-104)/(w^2) = (-104w^2)/(w^2) = -104/w^2
3) Now, we can combine the fractions:
(-4)/w + (-104)/w^2
4. Now, let's combine the remaining terms:
(-4 + (-104))/w + (-64) = (-108)/w - 64
5. Finally, simplify the expression:
(-108)/w - 64 is the simplified form of the given expression.
To summarize:
w - 2/w - 8 - w + 2/w + 8 + w - 104/w^2 - 64 simplifies to (-108)/w - 64.